<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:97"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="group_6.html#R1" target="_self">are_isomorphic</a> 
 <b>and </b><br/><a NAME="E2:97"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:97"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i><a class="txt" href="group_6.html#E1:97"><i><font color="Green">E70</font></i></a>, <a class="ref" href="group_6.html#D15" target="_self">Def15</a></i>;<br/>
<a NAME="E5:97"/>
<font color="Maroon">c<sub>3</sub></font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 
<b>by </b><i><a class="txt" href="group_6.html#E4:97"><i><font color="Green">E72</font></i></a>, <a class="ref" href="group_6.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E6:97"/><b>then </b><i><font color="Green">E73</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="group_6.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E7:97"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="group_6.html#E2:97"><i><font color="Green">E71</font></i></a>, <a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>
<a NAME="E8:97"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E9:97"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="group_6.html#E6:97"><i><font color="Green">E73</font></i></a>, <a class="ref" href="finset_1.html#T26">FINSET_1:26</a></i>;<br/>
<b>hence </b><a NAME="E10:97"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="group_1.html#V6">finite</a>
 <b>by </b><i><a class="ref" href="group_1.html#D14">GROUP_1:def 14</a></i>;<br/>


</div>
